"As a UK Government we remain absolutely steadfast in our commitment to the Belfast Agreement, its successor agreements."

Her comments follow warnings by the nationalist parties, Sinn Fein and the SDLP, and the cross-community Alliance Party, that a deal with the DUP would undermine the Government's attempts to restore the power-sharing executive at Stormont.

Mr Varadkar said he was reassured by the prime minister's commitment to make public the terms of any agreement.

"We spoke about the very important need for both governments to be impartial actors when it comes to Northern Ireland and that we are co-guarantors of the Good Friday Agreement and that any agreement that may exist between the Conservatives and the DUP should not in any way impact on the Good Friday Agreement," he said.

"I am very reassured by what the prime minister said to me today that that won't be the case."

The Conservatives have been in negotiations with the DUP since Mrs May lost her Commons majority in the General Election earlier this month.

A DUP source confirmed negotiations were "ongoing" and said they were looking to deliver "a more compassionate style of government for the whole of the UK".

The comments were seen as a coded reference to the party's opposition to scrapping the "triple lock" on pensions and means testing the winter fuel allowance - both of which were in the Conservative manifesto. It has also called for an end to the so-called "bedroom tax".

Both leaders expressed confidence that the Stormont institutions could be up and running again by the deadline of June 29, averting a return to direct rule from Westminster.

"It is my firm belief that with goodwill on both sides a resolution can be reached which builds on the progress made in the last round of discussions," Mrs May said.

Mr Varadkar said that restoring powersharing was particularly important with the start of the formal Brexit negotiations in Brussels.

"We think it is very important that Northern Ireland should have a unique voice at this very important time," he said.

"Having an executive up and running - an executive that can speak for both communities in Northern Ireland - would be a big advantage for Northern Ireland."

Both leaders re-affirmed their commitment to ensure that Britain's withdrawal from the EU did not lead to a return of a "hard border" between Northern Ireland and the Republic.

Mrs May said: "I am personally committed to ensuring a practical solution that recognises the unique economic, social, cultural and political context of the land border with Ireland, which so many people pass through every day, and it remains our priority to work closely with the Irish government to ensure as frictionless and seamless a border as possible."

Mr Varadkar added: "We want to make sure that there is minimal or no disruption to trade between our two countries.

"We want to ensure that as much as possible, while there many be a political border between our two countries, there should not be an economic border, and that any border that does exist should be invisible."

Senior DUP representative and former Stormont executive minister Simon Hamilton insisted any deal with the Conservative Party would benefit the whole of the UK, not just Northern Ireland.

Asked in Belfast if negotiations with the Tories would conclude this week, Mr Hamilton said: "They will take as long as they take.

"We are working away at them and will continue to work away at them. We are hopeful of getting resolution to them as quickly as we possibly can."